It's not entirely normal, but not entirely uncommon either. There probably isn't too much that can be done at this stage of pregnancy, if you are threatening a miscarriage, so I'm not sure that going to your doctor would help. Most of the time, they treat a single miscarriage as "these things just happen," and don't get worried unless you have multiple miscarriages (my sister's insurance wouldn't let her refer out to a high-risk specialist until after she had had three miscarriages!). My other sister bled some in the early stages of her first pregnancy, and she was understandably worried, but it turned out to be nothing (that baby just turned 10 years old).
If you call the doctor's office and explain what's going on, they will probably be able to get you in quicker; and I'm a little surprised they didn't schedule you earlier, since you have no idea how far along you are. Usually, they'll want to do an early ultrasound to verify dates, if the mom is unsure. The earlier in pregnancy they measure, the more accurate it is (within +/- 5 days in the first trimester; by the last trimester, it's only accurate to within two *weeks* before or after).
That said, I'm not a big fan of ultrasounds, especially the early ones. I know it would set your mind at ease and verify dates; but I don't like how that ultrasounds haven't really been studied to make sure there aren't any bad side effects from them. And most of the studies that have been done were done decades ago, and women are undergoing a lot more ultrasounds per pregnancy, starting earlier, using stronger equipment, etc., so there are a lot of variables that haven't even been taken into consideration.